超流体绕穿透障碍物涡旋脱落的动态相似性
Dynamic similarity of vortex shedding in a superfluid flowing past a penetrable obstacle
AI总结：
研究超流体绕穿透障碍物的涡街动力学，定义有效直径并构建超流体雷诺数，揭示涡旋脱落转变及斯特劳哈尔数与阻力系数的普适性。
摘要：
我们数值研究了超流体绕穿透障碍物的尾涡动力学。与不可穿透物体不同，穿透障碍物不会完全耗尽密度。我们从时间平均无旋流的音速1等高线定义有效直径D_eff，以界定局部超音速区域，其中量子涡旋成核。利用此流定义的长度尺度，我们构建了超流体雷诺数Re_s=(v_0 -v_c)D_eff/(ℏ/m)，其中v_0为流速，v_c为临界速度，m为粒子质量。我们表明Re_s组织了不同障碍物尺寸和强度下的尾涡动力学：从单极行发射到交替涡旋簇脱落的转变发生在Re_s约2时，当以Re_s为函数绘制时，斯特劳哈尔数和阻力系数均塌缩到普适曲线上。这些结果将超流体流动中的动态相似性概念扩展到穿透障碍物，并证明动态相关长度尺度由超音速区域决定，而非几何障碍物尺寸。
英文摘要：
We numerically investigate wake dynamics in a superfluid flowing past a penetrable obstacle. Unlike an impenetrable object, a penetrable obstacle does not fully deplete the density. We define an effective diameter $D_{\rm eff}$ from the Mach-1 contour of the time-averaged irrotational flow around the obstacle, which delineates the local supersonic region where quantized vortices nucleate. Using this flow-defined length scale, we construct a superfluid Reynolds number $Re_{\rm s} = (v_0 - v_c) D_{\rm eff}/ (\hbar/ m)$, where $v_0$ is the flow speed, $v_c$ is the critical velocity, and m is the particle mass. We show that $Re_{\rm s}$ organizes the wake dynamics across obstacle sizes and strengths: the transition from dipole-row emission to alternating vortex cluster shedding occurs at $Re_{\rm s}$ around 2, and both the Strouhal number and the drag coefficient collapse onto universal curves when plotted as functions of $Re_{\rm s}$. These results extend the concept of dynamic similarity in superfluid flows to penetrable obstacles and demonstrate that the dynamically relevant length scale is determined by the supersonic region rather than by the geometric obstacle size.
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